[FOM] Historical queries

[joeshipman@aol.com]

For each of the following theorems Xi, I need to know:

1) who first assumed Xi (that is, wrote something which makes no sense 
unless they believed Xi to be true even if they did not state it)
2) who first explicitly stated Xi as a known result or conjecture
3) who first wrote a proof of Xi

X1: Fundamental Theorem of Algebra (both existence and uniqueness of 
prime factorizations; but since existence is so easy, I will accept a 
statement of uniqueness; the important question is who first recognized 
that there is something that needs proving here)

X2: Irrationality of all square roots of integers that are not perfect 
squares (also, if anyone stated this for some infinite set of 
non-squares, such as "square roots of primes are irrational", I want to 
know this, because the theorem is easier to prove for primes than in 
general)

X3: Irrationality of all kth roots of integers that are not perfect kth 
powers, for all integers k>1 (or, again, if this was ever stated for 
some infinite subset, such as "the kth root of 2 is irrational for all 
k").

--JS
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